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        <meta name="DC.creator" content="Schäfer Aguilar, Paloma" />
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        <meta name="DC.creator" content="Ulbrich, Stefan" />
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        <meta name="DC.title" content="Convergence of numerical adjoint schemes arising from optimal boundary control problems of hyperbolic conservation laws" lang="en" />
        <meta name="citation_title" content="Convergence of numerical adjoint schemes arising from optimal boundary control problems of hyperbolic conservation laws" lang="en" />
        <meta name="title" content="Convergence of numerical adjoint schemes arising from optimal boundary control problems of hyperbolic conservation laws" lang="en" />
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        <meta name="DC.description" content="We study the convergence of discretization schemes for the adjoint equation arising in the adjoint-based derivative computation for optimal boundary control problems governed by entropy solutions of conservation laws. As boundary control we consider piecewise continuously differentiable controls with possible discontinuities at switching times, where the smooth parts as well as the switching times serve as controls. The derivative of tracking-type objective functionals with respect to the smooth controls and the switching times can then be represented by an adjoint-based formula. The main difficulties arise from the fact that the correct adjoint state is the reversible solution of a transport equation with discontinuous coefficient and boundary conditions that lead in general to discontinuous adjoints. Moreover, the solution of the adjoint equation is non-unique and the so-called reversible solution leads to the correct adjoint-based derivative representation.

We study discrete adjoint schemes of monotone difference schemes in conservation form such as Engquist-Osher or Lax-Friedrichs scheme. We also allow that the state is computed by another numerical scheme satisfying certain convergence properties. We proof convergence results of the discrete adjoint to the reversible solution." lang="en" />
        <meta name="description" content="We study the convergence of discretization schemes for the adjoint equation arising in the adjoint-based derivative computation for optimal boundary control problems governed by entropy solutions of conservation laws. As boundary control we consider piecewise continuously differentiable controls with possible discontinuities at switching times, where the smooth parts as well as the switching times serve as controls. The derivative of tracking-type objective functionals with respect to the smooth controls and the switching times can then be represented by an adjoint-based formula. The main difficulties arise from the fact that the correct adjoint state is the reversible solution of a transport equation with discontinuous coefficient and boundary conditions that lead in general to discontinuous adjoints. Moreover, the solution of the adjoint equation is non-unique and the so-called reversible solution leads to the correct adjoint-based derivative representation.

We study discrete adjoint schemes of monotone difference schemes in conservation form such as Engquist-Osher or Lax-Friedrichs scheme. We also allow that the state is computed by another numerical scheme satisfying certain convergence properties. We proof convergence results of the discrete adjoint to the reversible solution." lang="en" />
        <meta name="dcterms.abstract" content="We study the convergence of discretization schemes for the adjoint equation arising in the adjoint-based derivative computation for optimal boundary control problems governed by entropy solutions of conservation laws. As boundary control we consider piecewise continuously differentiable controls with possible discontinuities at switching times, where the smooth parts as well as the switching times serve as controls. The derivative of tracking-type objective functionals with respect to the smooth controls and the switching times can then be represented by an adjoint-based formula. The main difficulties arise from the fact that the correct adjoint state is the reversible solution of a transport equation with discontinuous coefficient and boundary conditions that lead in general to discontinuous adjoints. Moreover, the solution of the adjoint equation is non-unique and the so-called reversible solution leads to the correct adjoint-based derivative representation.

We study discrete adjoint schemes of monotone difference schemes in conservation form such as Engquist-Osher or Lax-Friedrichs scheme. We also allow that the state is computed by another numerical scheme satisfying certain convergence properties. We proof convergence results of the discrete adjoint to the reversible solution." lang="en" />
        <title>OPUS TRR154 | Convergence of numerical adjoint schemes arising from optimal boundary control problems of hyperbolic conservation laws</title>
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    <div about="Convergence of numerical adjoint schemes arising from optimal boundary control problems of hyperbolic conservation laws"><div id="titlemain-wrapper"><h2 class="titlemain" lang="en">Convergence of numerical adjoint schemes arising from optimal boundary control problems of hyperbolic conservation laws</h2></div><tr><th class="name">Submission Status:</th><td>under review</td></tr><div id="result-data"><div id="author"><p><a href="/opus4-trr154/solrsearch/index/search/searchtype/authorsearch/author/Paloma+Sch%C3%A4fer+Aguilar" title="Search for other publications by this author">Paloma Schäfer Aguilar</a>, <a href="/opus4-trr154/solrsearch/index/search/searchtype/authorsearch/author/Stefan+Ulbrich" title="Search for other publications by this author">Stefan Ulbrich</a></p></div><div id="abstract"><ul><li class="abstract preserve-spaces" lang="en">We study the convergence of discretization schemes for the adjoint equation arising in the adjoint-based derivative computation for optimal boundary control problems governed by entropy solutions of conservation laws. As boundary control we consider piecewise continuously differentiable controls with possible discontinuities at switching times, where the smooth parts as well as the switching times serve as controls. The derivative of tracking-type objective functionals with respect to the smooth controls and the switching times can then be represented by an adjoint-based formula. The main difficulties arise from the fact that the correct adjoint state is the reversible solution of a transport equation with discontinuous coefficient and boundary conditions that lead in general to discontinuous adjoints. Moreover, the solution of the adjoint equation is non-unique and the so-called reversible solution leads to the correct adjoint-based derivative representation.&#13;
&#13;
We study discrete adjoint schemes of monotone difference schemes in conservation form such as Engquist-Osher or Lax-Friedrichs scheme. We also allow that the state is computed by another numerical scheme satisfying certain convergence properties. We proof convergence results of the discrete adjoint to the reversible solution.</li></ul></div></div><div id="services" class="services-menu"><div id="download-fulltext" class="services"><h3>Download full text files</h3><ul><li><div class="accessible-file" title="Download file SchaeferAguilarUlbrichpapernumadjoint.pdf (application/pdf)"><a class="application_pdf" href="/opus4-trr154/files/481/SchaeferAguilarUlbrichpapernumadjoint.pdf">SchaeferAguilarUlbrichpapernumadjoint.pdf</a><img width="16" height="11" src="/opus4-trr154/img/lang/eng.png" class="file-language eng" alt="eng"/><div class="file-size">(456KB)</div></div></li></ul></div><div id="export" class="services"><h3>Export metadata</h3><ul><li><a href="/opus4-trr154/citationExport/index/download/docId/481/output/bibtex" title="Export BibTeX" class="export bibtex">BibTeX</a></li><li><a href="/opus4-trr154/citationExport/index/download/docId/481/output/ris" title="Export RIS" class="export ris">RIS</a></li><li><a href="/opus4-trr154/export/index/index/docId/481/export/xml/searchtype/id/stylesheet/example" title="Export XML" class="export xml">XML</a></li></ul></div><div id="additional-services" class="services"><h3>Additional Services</h3><div><a href="http://twitter.com/share?url=https://opus4.kobv.de/opus4-trr154/frontdoor/index/index/docId/481"><img src="/opus4-trr154/layouts/opus4/img/twitter.png" name="Share in Twitter" title="Share in Twitter" alt="Share in Twitter"/></a> <a href="http://scholar.google.de/scholar?hl=en&amp;q=&quot;Convergence of numerical adjoint schemes arising from optimal boundary control problems of hyperbolic conservation laws&quot;&amp;as_sauthors=Paloma+Sch&#xE4;fer Aguilar&amp;as_sauthors=Stefan+Ulbrich&amp;as_ylo=2021&amp;as_yhi=2021"><img src="/opus4-trr154/layouts/opus4/img/google_scholar.jpg" title="Search Google Scholar" alt="Search Google Scholar"/></a> <br/><a href="/opus4-trr154/frontdoor/mail/toauthor/docId/481">Send a mail to the author of this document</a></div></div></div><table class="result-data frontdoordata"><caption>Metadaten</caption><colgroup class="angaben"><col class="name"/></colgroup><tr><th class="name">Author:</th><td><a href="/opus4-trr154/solrsearch/index/search/searchtype/authorsearch/author/Paloma+Sch%C3%A4fer+Aguilar" title="Search for other publications by this author">Paloma Schäfer Aguilar</a>, <a href="/opus4-trr154/solrsearch/index/search/searchtype/authorsearch/author/Stefan+Ulbrich" title="Search for other publications by this author">Stefan Ulbrich</a></td></tr><tr><th class="name">Document Type:</th><td>Preprint</td></tr><tr><th class="name">Language:</th><td>English</td></tr><tr><th class="name">Date of Publication (online):</th><td>2021/12/13</td></tr><tr><th class="name">Release Date:</th><td>2021/12/13</td></tr><tr><th class="name">Institutes:</th><td><a href="/opus4-trr154/solrsearch/index/search/searchtype/collection/id/16219" title="Browse collection">Technische Universität Darmstadt</a></td></tr><tr><th class="name">Subprojects:</th><td><a href="/opus4-trr154/solrsearch/index/search/searchtype/collection/id/16229" title="Browse collection">A02</a></td></tr></table></div>

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